Positive integer solutions of certain diophantine equations

  • Bijan Kumar Patel
  • Prasanta Kumar Ray
  • Manasi K Sahukar
Article
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Abstract

In this study, the diophantine equations \(x^2 -32B_nxy-32y^2 =\pm 32^{r}\), \(x^4 -32B_nxy-32y^2 =\pm 32^{r}\) and \(x^2 -32B_nxy-32y^4 =\pm 32^{r}\) are considered and determined when these equations have positive integer solutions. Moreover, all positive integer solutions of these diophantine equations in terms of balancing and Lucas-balancing numbers are also found out.

Keywords

Diophantine equations balancing numbers balancers Lucas balancing numbers 

2010 Mathematics Subject Classification

11B37 11B39 11D45 

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  • Bijan Kumar Patel
    • 1
  • Prasanta Kumar Ray
    • 2
  • Manasi K Sahukar
    • 3
  1. 1.International Institute of Information TechnologyBhubaneswarIndia
  2. 2.VSS University of Technology, OdishaBurlaIndia
  3. 3.National Institute of TechnologyRourkelaIndia

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